HH is a nervous system issue (neurology), NOT a skin issue (dermatology).
Dermatologists are trained on HH via education programs and readings/seminars, not in their medical training. Dermatologists will usually give out things like anti-perspirates (deodorants), creams, etc, which do not assist the nervous system to slow down (HH is caused by an over sympathetic nervous system). They can give botox (in most countries), but that's about where their expertise stops - they know less about the system that causes HH (nervous system). Dermatologists are more for people who just sweat a lot rather than actual HH (they are NOT the same thing).
So, if you have HH really badly and go to a dermatologist, they will offer the above stuff that may or may not work, you pay for all that, then if it doesnt work, they will eventually refer you to a neurologist anyway, and youll pay for it all again. Meanwhile, months possibly years will pass.
If you go to a neurologist in the first place, they are medically trained in HH as it is directly in their area of expertise, AND they can give you all of the above (deodorants, creams, botox) PLUS a heck of a lot of other options, such as CTS and medications etc. They will understand the source better than a dermatologist.
Sorry if you already knew all that I just felt a need to explain it lol
If it was me, Id probably go to a neurologist because I hate ****ing around, but chat to your doctor about it and do whatever youre comfortable with.
In the UK you MUST see your GP to get a referral to a speci*list on the NHS (I get around and have had speci*list treatment in the UK before, if anyone is confused).
Its perfectly ok and normal to ASK your GP to refer you, tell him it would need to be via the NHS when you do. Ive never come across a GP who has any issue with refering people at all - if a treatment isn't working, they are usually glad to refer you on to someone else, so don't be worried about asking.